The definition of a Courant algebroid can be given using two different bracket operations:
the Courant bracket \(\llbracket \cdot ,\cdot \rrbracket _{\rm Cour}\)  or the Dorfman bracket \(\llbracket \cdot ,\cdot \rrbracket \) .
The difference is that one can require the bracket either to be skew-symmetric (Courant) or to satisfy
the Jacobi identity (Dorfman), but not both.
The original definition, introduced in [1]}, is in terms of the Courant bracket.
The two brackets are related by
\(\llbracket X,Y \rrbracket _{\rm Cour}=\tfrac{1}{2}(\llbracket X,Y\rrbracket -\llbracket Y,X\rrbracket )\) .
